Supplementary Materials for the article:

Beyond glass transitions: Studying the highly viscous and elastic behavior of frozen protein formulations using low temperature rheology and its potential implications on protein stability

Jian Hua Gu1, Alice Beekman1, Tian Wu2, Deirdre Murphy Piedmonte1, Priti Baker1, Michael Eschenberg3, Michael Hale3 and Merrill Goldenberg1*

1 Drug Product Development, Process and Product Development

2 Pharmaceutical R&D, Small Molecule Process and Product Development

3 Medical Sciences Biostatistics

Amgen Inc. Thousand Oaks, CA 91320

* Corresponding Author:

Merrill Goldenberg

Drug Product Development

Process and Product Development

Amgen Inc., MS 8-1-C

One Amgen Center Drive

Thousand Oaks, CA 91320, USA

e-mail:

Appendix I Statistical Evaluation of Aggregate Formation

Statistical Methods

The evaluation of rate of change for the % pre-peak area (percent of aggregates) was performed using an analysis of variance (ANOVA) model. For the comparison of aggregate formation rate between temperatures for 70 mg/mL material, a random effects model was employed with week, temperature, and the week by temperature interaction included as fixed effects while lot and lot by temperature by week interaction included as random effects. For the evaluation of aggregate formation rate between material concentration at -10°C (20, 30, 40, and 70 mg/mL) and for the evaluation of aggregate formation rate between material condition at -10°C (staged frozen, non-staged froze, and non-staged liquid) a fixed effects model was employed for each evaluation with week, concentration (or material condition), and the week by concentration (or material condition) interaction included in the model as fixed effects.

For each ANOVA performed, an evaluation of the slope for the regression line was made to determine whether the same slope (homogeneity of slopes) should be applied to the regression line for each level of the fixed effects factor of interest (i.e., temperature, concentration or material condition). If the p-value associated with the test of homogeneity of slopes was found to be less than 0.05 (statistically significant), paired comparisons for each level of the fixed effects factor of interest was performed to evaluate the differences in the rate of aggregate formation between the factor levels.

Results

Percent Pre-Peak Area of IgG2 at 70 mg/mL at Different Storage Temperatures

The results of the ANOVA for the percent pre-peak area of IgG2 at 70 mg/mL demonstrated a statistically significant difference in the rate of aggregate formation based on the storage temperature (p<0.0001). Four unique lots of material were included in the analysis. Each lot of material included a single observation (measurement of aggregate) for multiple temperatures at each assessment (week), although all lots of material may not have been measured at the same weeks. The results of the paired comparisons are included in Table AI.1. The results demonstrate that the rate of aggregate formation is statistically significantly higher (larger slope) at the 25°C storage temperature compared to each of the other storage temperatures. Additionally, the rate of aggregate formation is statistically significantly higher at the -10°C storage temperature compared to the 4°C, the -15°C, and the -20°C storage temperatures. None of the other comparisons reached statistical significance.

Figures AI.1 and AI.2 show the results graphically for all the data. AI.1 shows the data without any attempt to normalize for the variability of aggregate in the starting material (note error bars at t0). Figure AI.2 normalizes for this variation in the starting material.

Table AI.1. Estimated Difference in Aggregate Formation Rates at Different Storage Temperatures for 70 mg/mL Material /
Storage Temperatures Comparisons / Estimated Difference in Slope / Standard Error of Estimated Difference / Degrees of Freedom / t-Value / p-value /
-10°C vs. -15°C / 0.01959 / 0.004491 / 23.4 / 4.36 / 0.0002
-10°C vs. -20°C / 0.02765 / 0.004986 / 25.5 / 5.55 / <.0001
-10°C vs. 25°C / -0.01761 / 0.005398 / 21.3 / -3.26 / 0.0037
-10°C vs. 4°C / 0.02403 / 0.004978 / 25.4 / 4.83 / <.0001
-15°C vs. -20°C / 0.008057 / 0.004993 / 25.7 / 1.61 / 0.1188
-15°C vs. 25°C / -0.03720 / 0.005404 / 21.4 / -6.88 / <.0001
-15°C vs. 4°C / 0.004433 / 0.004985 / 25.5 / 0.89 / 0.3821
-20°C vs. 25°C / -0.04525 / 0.005793 / 22.8 / -7.81 / <.0001
-20°C vs. 4°C / -0.00362 / 0.005403 / 26.7 / -0.67 / 0.5081
25°C vs. 4°C / 0.04163 / 0.005787 / 22.7 / 7.19 / <.0001

Percent Pre-Peak Area of IgG2 at -10°C for Different Concentrations

The results of the ANOVA for the percent pre-peak area of IgG2 at -10°C demonstrated a statistically significant difference in the rate of aggregate formation based on material concentration (p<0.0001). A single lot of material was available and used for the statistical analysis with a single observation for each concentration at each assessment (week). The results of the paired comparisons of the rate of aggregate formation are included in Table AI.2. The results demonstrate that the rate of aggregate formation is statistically significantly different between each concentration pair except for the comparison between 20 mg/mL and 30 mg/mL, whose difference did not reach statistical significance. A general observation is that as the concentration of material increases, the rate of aggregate formation increases.

Table AI.2. Estimated Difference in Aggregate Formation Rates at -10° C for Different Concentrations of Material /
Concentration Comparison / Estimated Difference in Slope / SE for Estimated Difference / Degrees of Freedom / t-Value / p-value /
20mg/mL vs. 30mg/mL / -0.00054 / 0.002891 / 16 / -0.19 / 0.8542
20mg/mL vs. 40mg/mL / -0.01666 / 0.002891 / 16 / -5.76 / <.0001
20mg/mL vs. 70mg/mL / -0.03333 / 0.002891 / 16 / -11.53 / <.0001
30mg/mL vs. 40mg/mL / -0.01612 / 0.002891 / 16 / -5.58 / <.0001
30mg/mL vs. 70mg/mL / -0.03279 / 0.002891 / 16 / -11.34 / <.0001
40mg/mL vs. 70mg/mL / -0.01666 / 0.002891 / 16 / -5.76 / <.0001

Percent Pre-Peak Area of IgG2 for Different Material Status

The results of the ANOVA for the percent pre-peak area of IgG2 based on the material condition (staged frozen, non-staged frozen, non-staged liquid; each at -10°C) demonstrated a statistically significant difference in the rate of aggregate formation based on material condition (p<0.0001). A single lot of material was used for the analysis with a single observation for each material condition at each assessment (week). The results of the paired comparisons are included in Table AI.3. The results demonstrate that the rate of aggregate formation is statistically significantly lower for the non-staged liquid compared to each of the other material conditions. The difference in rate of aggregate formation between the non-staged frozen and the staged frozen did not reach statistical significance.

Table AI.3. Estimated Difference in Aggregate Formation Rates at -10° C for Different Material Conditions /
Material Comparison / Estimated Difference in Slope / SE for Estimated Difference / Degrees of Freedom / t-Value / p-value /
Non-Staged Frozen vs. Non-Staged Liquid / 0.03764 / 0.006313 / 12 / 5.96 / <.0001
Non-Staged Frozen vs. Staged Frozen / -0.00329 / 0.006313 / 12 / -0.52 / 0.6119
Non-Staged Liquid vs. Staged Frozen / -0.04093 / 0.006313 / 12 / -6.48 / <.0001

Figure AI.1 illustrates the average percent of aggregate at each temperature by assessment week with bars representing the standard deviation. When an assessment week for a given temperature had only one lot of material evaluated, the observed value for the single lot is graphed with no bars.

Figure A1.1 Percent Aggregate (Mean ± SD) by Study Week Across Lots of Material

Figure AI.2 illustrates the average percent change from baseline of the percent aggregate with bars representing the standard deviation of the percent change from baseline. When an assessment week for a given temperature had only one lot of material evaluated, the percent change from baseline for the single lot is graphed with no bars.

Figure A1.2 Aggregate Percent Change From Baseline (Mean ± SD) by Study Week Across Lots of Material

Appendix II Rheology of Frozen Sucrose Solutions

Sucrose solutions above the very low concentration of 0.08% (w/v) exhibited very different behavior from the water, salt solutions and protein in water. Figure S.1 shows that at the higher concentrations (2 to 9% w/v), the melting curve showed two softening temperatures: a principal one near -32°C, which matches the literature Tg’ for a maximally freeze-concentrated solution (1), and a secondary one at higher temperature, somewhat variable in the range of -5°C to -15°C, that preceded the water melt near 0°C. After the initial softening, beginning at Ts*, there was a partial rehardening, ~10-fold increase in G*, that began about -20°C for the 9% sucrose sample, followed by a secondary softening (Ts2*) that began at the secondary G* peak near -15°C. The resulting dip in the G* profile was variable in magnitude. The temperature of the secondary rehardening peak varied with concentration (in the range 2 to 9%) from -5°C to -15°C, and appeared to be the development of viscoelastic structure, as there was a pronounced drop in the phase angle. The shear modulus (G*) of these hardening and softening events, ~105 Pa to ~106 Pa is similar to that of synthetic rubbers (2) and hard dairy products such as cooled butter (3) or aged cheese (4). Between 2% and 1.6% sucrose there was an abrupt change in the profile. There was no fall in G* for 1.6% sucrose at -32°C and the Ts* for 1.6% sucrose occurred near the Ts2* for the higher sucrose concentration. At 0.08% sucrose, the G*-thermal curve was similar to pure water. As discussed in the main text, the melting curve for the full placebo formulation (G* in Figure S.2) was very similar to that for 9% sucrose. Ts2* occurred within a few degrees of -15°C, depending on several factors including hold time, and exhibited similar variability in the degree of initial softening.

Extensive dilution (to ~0.08% sucrose) was required to obtain a G* profile resembling water, but between 2.0% to 1.6%, there was a striking change intermediate between pure water and the “dip” profile discussed above. This small decrease in concentration caused the Ts* to rise much higher than the Tg’ so that it coincided with the Ts2* of the more concentrated solutions. DSC studies (5) have been able to measure the Tg’ of solutions as dilute as 0.14% and have found that the Tg’ was still -32°C. As was noted above, in the polymer literature, Tg as measured by DSC and rheological testing do not always coincide.

However, it was puzzling that the divergence of Ts* and Tg’ occurred so strongly and abruptly over a narrow concentration range. Two possible explanations are: 1) the initial G* of the rubbery phase was off the scale that we could measure (i.e., the Ts* is overestimated) with the current geometry of our apparatus, or 2) there was a percolation threshold for softening of the mosaic of ice and interstitial rubbery regions. Regarding the first explanation, it would mean that the initial G* of the rubber was very high (> 3MPa), at the very high end of reported glass/rubber transitions and likely very restricted molecular movement. Also, it does not explain why the change occurred so abruptly with concentration, which percolation theory can explain more specifically, a certain critical level of freeze concentrate was required to lubricate the surfaces of the ice particles. For the stress levels in these experiments, < 0.1 MPa, Xu (6) has shown that the only possible movement occurs at the boundaries of the ice grains. If there is insufficient freeze concentrate to fill a network of channels around the ice grains, the ice grains are locked and the G* is very high. A related phenomenon is seen in diverse fields such as drug delivery and mechanical properties of filled composites where sudden changes in properties can be explained by percolation theory (7). For example, in drug delivery from a solid water-insoluble matrix, the water soluble drug particles at low concentration have no path to the matrix surface and are essentially locked in and cannot flow into the surrounding fluid. At a certain critical concentration, i.e., ~10-15 volume%, the particles suddenly come into contact with each other creating channels to the surface and thereby can be released. Similarly, the mechanical properties of a composite with voids would suddenly drop once a critical level of voids is reached. We speculate the dramatic change of Ts* between 2.0 and 1.6% sucrose may be explained by percolation theory whereby at ~2% sucrose the freeze concentrate just coats the ice blocks allowing mechanical movement at a significantly lower temperature than at 1.6% sucrose.

Appendix III Different Estimates of Tg’

In addition to G*, Figure S.2 compares different estimates of the temperature transition, T, for the placebo formulation. The two G’’ maxima offers insight into potential protein instability of a formulation. The shape of the G’’/T curve is a balance between the thermal mobility of the components in the formulation and the frictional effects of the components sliding by one another and thus leading to higher protein/protein contacts. A peak in the G’’ represents the temperature at which the maximum amount of frictional heat is lost by the sample in that temperature region. The first G’’ maximum occurs a few degrees higher than Ts* and would represent a temperature where contacts can begin to occur. The second G’’ maximum occurs at ~-10°C for both the 70 and 40 mg/mL formulations and this is the temperature that shows the highest degree of instability tested for these formulations and where ice surfaces play an important role. We speculate that the T(G’’max) may turn out to signal a point at which protein instability greatly accelerates, assuming that the protein is at a sufficiently high concentration (perhaps >30 mg/mL). At lower protein concentrations, as noted above, sucrose protects the protein.

Appendix IV Intermolecular Travel/Distance Calculations

Calculations of root mean square distance traveled at -10°C by Brownian motion (distance x in one dimension, where x=(Dt)1/2 and D=kT/(6phr), h at -10°C taken to be on the order of 106 Poise; t=time in sec; T=temperature; D=diffusion coefficient; k=Boltzmann’s constant) indicate the mAbs could travel several hundred nm (20 or more molecular diameters) in one week. This distance is large compared to the average distance between molecules at 210 mg/mL (3-fold freeze concentration at this temperature) of 10nm, one molecular diameter apart. There is no one method to calculate the average distance between centers of the molecules but it can readily be shown that a rough estimate of that distance is V1/3, (V=volume available per molecule) (8,9), and, using correction factors based on actual packing of spheres, approximate near that for tetrahedral packing, i.e. at 0.86 V1/3 , which is the estimate we used.